Question

The line AB had midpoint (2, 5).

A has coordinates (1, 2).

Find the coordinates of B.

Answer 1

The line AB, with A(Ax, Ay), B(Bx, By) and midpoint M(Mx, My) satisfying:

Ax + Bx = 2Mx

Ay + By = 2My

=>

2 + Bx = 2*1

5 + By = 2*2

=> Bx = 0

=> By = -1

=> B(0, -1)

Hope this helps!

:)

Answer 2

B(3, 8 )

Explanation:

Using the midpoint formula

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then midpoint is

[
`(1)/(2)`(x₁ + x₂ ),
`(1)/(2)`(y₁ + y₂ ) ]

let the coordinates of B = (x, y ), then

`(1)/(2)`(1 + x) = 2 ( multiply both sides by 2 )

1 + x = 4 ( subtract 1 from both sides )

x = 3

and

`(1)/(2)` (2 + y) = 5 ( multiply both sides by 2 )

2 + y = 10 ( subtract 2 from both sides )

y = 8

Thus

coordinates of B = (3, 8 )